They were not injured but were very cold and were airlifted to Whakatane Hospital to be assessed, a St John Ambulance spokesman said.
One Waimana local, who did not wish to be identified, said the vehicle was submerged up to its windows.
The current was flowing fast and had turned the van about 90 degrees.
The road between Opotiki and Whakatane and the road between Opotiki and Taneatua are closed due to flooding, and water levels are still rising.
Police said it would be some time before the water subsides and roads are clear again.
Motorists travelling north from the Rhythm and Vines Concert in Gisborne were urged to travel via Napier and then Taupo rather than through Waimana Gorge to Opotiki.
Meanwhile, a mother and her three young children are trapped in a house due to flooding just to the south.
Their house is surrounded by water from Waimana River.
They were safe so emergency services were waiting for the water level to drop before they tried to get to them, Fire Service shift manager Jaron Phillips said.
A house in nearby Kawerau also had to be pumped due to the flooding.